If f(x) = -8m + 3 and g(x) = -8m^2 + m - 5, what is (f times g)x?

A.) 64m^3 - 16m^2 + 43m - 15
B.) 64m^3 +43m - 15
C.) 64m^3 - 32m^2 + 43m - 15
D.) -16m^2 + 43m - 15

Answers

Answer 1

Answer:  Choice C

[tex]64m^3-32m^2+43m-15[/tex]

==================================================

Explanation:

Multiply out the expressions using the distribution rule as shown below.

[tex](-8m+3)(-8m^2+m-5)\\\\n(-8m^2+m-5) \ \ \text{ ... see note1}\\\\-8m^2n+mn-5n\\\\-8m^2( n )+m( n )-5( n )\\\\-8m^2( -8m+3 )+m( -8m+3 )-5( -8m+3 ) \ \ \text{ ... see note2}\\\\( 64m^3-24m^2 )+( -8m^2+3m )+( 40m-15 )\\\\64m^3+(-24m^2-8m^2)+(3m+40m)-15 \\\\64m^3-32m^2+43m-15 \\\\[/tex]

I used the tool WolframAlpha to confirm the answer is correct. GeoGebra is another free tool that offers similar capabilities.

Footnotes:

Note1: I let n = -8m+3, and replaced -8m+3 with n. That way the distribution on the next step could happen.Note2: I plugged in n = -8m+3. After which distribution happens 3 more times.

Related Questions

Here is an equation: 4y - 6x = 12

Is (-4, -3) a solution? Is (0, 3) a solution?

Answers

If the equation is 4y - 6x = 12, then (-4, -3) and (0, 3) are the solutions of the equation

The equation is given that

4y - 6x = 12

The first solution =(-4, -3)

The value of x = -4

The value of y = -3

Substitute the values in the equation

4(-3) - 6(-4) = 12

-12 - (-24) = 12

-12 + 24 = 12

12 = 12

Therefore (-4, -3) is the solution of the equation

Next solution is (0, 3)

The value of x = 0

The value of y = 3

Substitute the values in the equation

4(3) - 6(0) = 12

12 - 0 = 12

12 = 12

Therefore (0, 3) is the solution of the equation

Hence, if the equation is 4y - 6x = 12, then (-4, -3) and (0, 3) are the solutions of the equation

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Given m/PSR = 134, find m/SQR.

Answers

The measure of the angle SQR is 68 degrees if m/PSR = 134 and Angle QPS = Angle PSQ  = Angle SQP = 60 degrees.

What is an angle?

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

It is given that:

m/PSR = 134,

PQ = QS = PS

Angle QPS = Angle PSQ  = Angle SQP = 60 degrees

Angle QSR = QRS

Angle SQR = 180 - (180 - 134)x2

= 180 - 112

= 68 degrees

Thus, the measure of the angle SQR is 68 degrees if m/PSR = 134 and Angle QPS = Angle PSQ  = Angle SQP = 60 degrees.

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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is placed. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Use the rules of exponents to evaluate or simplify. Write without negative exponents.

(bm)⁻³

Answers

The expression can be written without negative exponents as 1/(bm)³

Simplification of Exponents

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. This can be written as 6⁴. Here, 4 is the exponent and 6 is the base.

Simplifying exponents is a method of simplifying the algebraic expressions involving exponents into a simpler form such that they cannot further be simplified. There are rules in algebra for simplifying exponents with different and same bases that we can use.

Steps to removing exponents are;

Step 1

remove parentheses by multiplying factors.

Step 2

use exponent rules to remove parentheses in terms with exponents.

Step 3

combine like terms by adding coefficients.

Step 4

combine the constants.

In this case, we have an expression;

(bm)⁻³ which can be rewritten using cube.

(bm)⁻³ = 1/ (bm)³

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Find the sum.
10+30+50+...+(20n-10)

Answers

Answer:

10

Step-by-step explanation:

tbh i am confused

please if you see this, i am really trying my best and you guys gave me the hardest question i ever had. sincerely apologize

(2x² - 6x + 5) + (7x²-x-9)

need help finding sum or difference

Answers

Answer:

the answer is either x= 4 , or it is   9[tex]x^{2} \\[/tex] - [tex]x[/tex] - 10

Step-by-step explanation:

Sorry dude, I'm confused a little bit on what to do, but i think one of these is right.

lmk if you get it right, and which one you used

Can you remember why a perfectly competitive firm faces a perfectly elastic demand curve?.

Answers

Since they take prices rather than setting them, fully competitive enterprises must deal with a completely elastic demand curve.

What is competitive firm?

A perfectly competitive firm is a price taker, which means that it must accept the equilibrium price at which it sells goods. If a perfectly competitive firm attempts to charge even a tiny amount more than the market price, it will be unable to make any sales.

Since they take prices rather than setting them, fully competitive enterprises must deal with a completely elastic demand curve. They are so unable to alter the market selling price. In order to raise its income, a perfectly competitive firm will therefore increase output rather than pricing.

A totally competitive firm is unable to arbitrarily set its output price since it must accept the price set by the product's market demand and supply. As an alternative, the perfectly competitive firm can decide to sell any amount of output for the same price. Because customers are eager to purchase any quantity of the company's output at the market price, it follows that the firm must deal with a completely elastic demand curve for its product. The quantity that the perfectly competitive firm decides to produce, combined with the prices that are in effect on the market for inputs and outputs, will determine the firm's total revenue, total costs, and eventually the level of profits.

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part a, b, c.
with explanation please:)

Answers

Answer:

a.

Equation 1: y = x + 1

Equation 2: y = 4x - 5

Substitute Equation 1 into Equation 2:

x + 1 = 4x - 5

Now, solve for x:

4x - x = 1 + 5

3x = 6

x = 2

So now we have x, lets solve for y:

y = x + 1

Substitute x:

y = 2 + 1

y = 3

So the point of intersection of line y = x + 1 and line y = 4x -5 is (2,3) as shown on the graph.

Lets do the other two now:

b.

Equation 1: x + 4y = 1

Equation 2: 2x - y = -7

For this one we cannot simply substitute we have to get rid of one variable to create another equation.

Lets get rid of x for equation 3. To do this we simply times Equation 1 by 2:

Equation 3: 2x + 8y = 2

With this we can minus Equation 2 and Equation 3 to get rid of x:

2x - y = -7

-

2x + 8y = 2

-9y = -9

y = 1

Now that we have the y value, we can now find x using any equations above, lets use Equation 1:

x + 4y = 1

x + 4(1) = 1

x + 4 = 1

x = 1 - 4

x = -3

So the point of intersection is (-3,1).

c.

Equation 1: 4x + y = 11

Equation 2: y = -2x + 3

For this question, we can just do what we did for question a.

Lets substitute Equation 2 into Equation 1:

4x + (-2x + 3) = 11

4x - 2x + 3 = 11

2x + 3 = 11

2x = 11 - 3

2x = 8

x = 4

So we got our x value, let get our y value. Lets use Equation 1 for that:

4x + y = 11

4(4) + y = 11

16 + y = 11

y = 11 - 16

y = -5

So, the point of intersection is (4,-5).

use the median income 27 and 29 years old to write an equation in slope intercept from of the line of fit​

Answers

Answer: ?

Step-by-step explanation:

that's how you do it.

Austen's retirement party will cost $10 if he invites 5 guests. If there are 7 guests, how much will Austen's retirement party cost? Solve using unit rates.

Answers

Answer: $14

Step-by-step explanation:

First, find the amount it will cost with one guest(x):

[tex]\frac{10}{5} =\frac{x}{1} \\\\10=5x\\\\x=\frac{10}{5} =2[/tex]

Then, use ratios to find the amount it will cost with seven guests(y):

[tex]\frac{2}{1} =\frac{y}{7} \\\\y=14[/tex]

Not sure if this is how you want it to be solved.

The price of an item has been reduced by 20%. The original price was $86.

Answers

Step-by-step explanation:

item on sale costs 60 % of the original price

(sale price) = 60% of (original price)

(sale price) = 60% of $85

[given: (original price) = $85

(sale price) = $(60/100)*85

[60% may be written as 60/100 or 0.60 as needed by the problem]

(sale price) = $51.00

The price of this item must be 68.80

A shipment service provides uses three types of containers for shipping materials the height and width of the three container are the same the containers height is 0.15 m more than their width and volume of the smaller container is 652 m³

1) write a polynomial relating container 1 length, breadth and height with its volume?

Answers

The polynomial representing length, breadth and height of th e container is

Lw^2 + 0.15Lw - 652

How to find the polynomial relating the dimensions of the container

Volume is measure in liters, cubic meters and so on

The formula for volume calculation is given by

volume = length * width * height

from the question

height is 0.15 m more than their width

width = w

height = 0.15 + w

length = L

volume = 652 m³

652 = L * w * (w + 0.15)

652 = (w^2 + 0.15w)L

652 = Lw^2 + 0.15Lw

Lw^2 + 0.15Lw - 652

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When testing the difference between two population means, the sample variances are pooled to estimate the population variance when ________________.

The population means are known
The population variances are assumed equal but unknown
The population variances are known and equal
The population variances are assumed unequal and unknown

Answers

When testing the difference between two population means, the sample variances are pooled to estimate the population variance when The population variances are assumed equal but unknown.

Population Mean:

The population mean can be calculated by the sum of all values in the given data/population divided by a total number of values in the given data/population.

In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are: n1 + n2 - 2.

population variance:

Population variance is a measure of how spread out a group of data points is. Specifically, it quantifies the average squared deviation from the mean.

Therefore When testing the difference between two population means, the sample variances are pooled to estimate the population variance when The population variances are assumed equal but unknown.

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Please do the one you are able to do anything is helpful!

Answers

Answer:

9. train a = 8.33 hours

train b = 5 hours

time of coincidence = 3.33 hours

Step-by-step explanation:

I'm not sure about this but I think it's correct.

4h + 3 = 6h - 15
h =

Answers

Answer:

h = 9

Step-by-step explanation:

Step 1: Subtract 6h from both sides.

4h +3 −6h = 6h −15 −6h

−2h +3 = −15

Step 2: Subtract 3 from both sides.

−2h + 3 −3 = −15 −3

−2h = −18

Step 3: Divide both sides by -2.

(-2h/-2) = (-18/-2)

h = 9

NEED HELP ASAP, EXPLANATION WOULD BE APPRECIATED

Answers

Answer:

x=7/10

Step-by-step explanation:

Because this is a square, we know that all of the sides are equal.

Thus, we know that 6x-1=4x+6.

We can further use Algebra and subtract by 4x on both sides.

Now, we have 10x-1=6.

Then, we can add 1 to both sides, and get 10x=7.

Lastly, let's divide both sides by 10 to isolate x, getting x=7/10, or x=0.7

-1.3 + u/4 = -7.7 solve for u

Answers

Answer:

[tex]u=-25.6[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=530(1.04)x

Answers

The given exponential function will grow at rate of 4%

Given, the following exponential function,

y = 530(1.04)ˣ

we are asked to  identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

we have:

y = 530(1.04)ˣ

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is:

y(x) = a(1-r)ˣ

⇒ 1+r = 1.04

⇒ r = 0.04

⇒ r = 4%

Hence the given exponential function will grow at 4%.

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pls help urgent!

Solve for the roots in simplest form using the quadratic formula:

x²-16x = -100

Answers

Answer:

x has no real solution/roots

Step-by-step explanation:

please see the attached image:

A _____________ t-test evaluates data from dependent samples in which the two treatments are applied to the same individual.

Answers

A Paired t-test evaluates data from dependent samples in which the two

treatments are applied to the same individual.

T-test is a statistical statistics mainly use when population variance is

unknown and sample size is small.

In Paired t-test , we compare means of two dependent samples. It gives

hypothesis examination on difference between of mean.

It uses same items or people in both sample that's why they are also known as dependent t-test or Paired t-test also increases the statistical power of our analysis.

Formula of paired t-test :

t = m / S / n

with (n-1) degree

where , m --> mean difference

S ---> standard deviation difference

n --> sample size

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I need help with this

Answers

f(x)-g(x)
= 2√m - 3√4m
= 2√m - 3*2√m
= 2√m - 6√m
= -4√m

Hope this helps

you and your friends went to dinner together and ordered 4 hamburgers at $5.95 each, 3 baskets of fries at $4.25 each, and 4 sodas at $1.75 each. how much was the total for all of the food and drink?

Answers

Using the concepts of unitary method, we got that  $42.83 was the total for all of the food and drink. if me and my friend went to dinner together and ordered 4 hamburgers at $5.95 each, 3 baskets of fries at $4.25 each, and 4 sodas at $1.75 each

Since, we are given that cost price of one hamburger is $5.95,

so total cost of 4 hamburgers is =4×5.95=$23.08

Similarly, we are given that cost price of one baskets of fries which is $4.25,

so total cost of three baskets of fries is =3×4.25=$12.75

Similarly, we are given that cost price of one soda which is $1.75,

so total cost of 4 soda  is =4×1.75=$7.00

So, Total cost of my order is= 4 hamburger cost+3 baskets of fries cost +4 sodas cost =23.08+12.75+7.00=$42.83

Hence, if me and my friends went to dinner together and ordered 4 hamburgers at $5.95 each, 3 baskets of fries at $4.25 each, and 4 sodas at $1.75 each, the total for all of the food and drink was $42.83

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This sign was in a doctor's waiting room. 115 appointments were missed last month. These missed appointments were a total of 25.3 hours. Work out the mean length of time for each missed appointment. Give your answer in minutes.​

Answers

The mean length of time for each missed appointment in minutes will be 13.2 minutes per missed appointment.

What is Mean?

The mean is the simple definition of the average of a large number. This actually implies one of the indicators of focused tendency in measurements. The statistic means is referred to as the normal. It is the ratio of the number of true judgments to the total number of impressions.

This sign was in a specialist's sitting area. 115 arrangements were missed a month ago. These missed arrangements were a sum of 25.3 hours.

The total number of minutes is given as,

⇒ 25.3 hours

⇒ 25.3 x 60 minutes

⇒ 1,518 minutes

The mean length of time for each missed appointment in minutes will be given as,

⇒ 1,518 / 115

⇒ 13.2 minutes per missed appointment

The mean length of time for each missed appointment in minutes will be 13.2 minutes per missed appointment.

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9^3 in standard form

Answers

Answer:

729! Hope this helps :)

Step-by-step explanation:

Answer:

9^3 in standard form

Step-by-step explanation:

9 × 9 × 9

81 × 9

729

Maryanne invests $500 into an account that earns 4% annual interest compounded quarterly.

What is her account balance after 5 years if she makes no withdrawals or deposits?

Enter your answer in the box.

Answers

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=500\left(1+\frac{0.04}{4}\right)^{4\cdot 5} \implies A=500(1.01)^{20}\implies A \approx 610.10[/tex]

An appliance technician charges a fixed amount for a repair, plus an additional amount per hour. The equation below describes y, the total amount the technician charges, in dollars, for a repair that takes x hours. y = 20x + 50
What is the meaning of the y-intercept of the equation?
A. It means the technician charges a fixed amount of $20 for the repair. B. It means the technician charges $50 per hour for the repair.
C. It means the technician charges $20 per hour for the repair.
D. It means the technician charges a fixed amount of $50 for the repair.

Answers

The y-intercept of the equation means: D. It means the technician charges a fixed amount of $50 for the repair.

How to Interpret the Y-intercept of an Equation?

The y-intercept of an equation that models a situation is the initial or starting value. The y-intercept is represented in an equation that is expressed in slope-intercept form, y = mx + b, as "b". The value of "b" is the y-intercept.

Therefore, we are given that y = 20x + 50 represents the total amount the technician charges, in dollars, for a repair that takes specific hours. This implies that:

x = hoursy = total amountm = 20, which is the additional amount per hour.b = 50 = y-intercept, which is the starting value that represents the fixed amount for a repair that the technician charges.

Therefore, y-intercept, b = 50, means: D. It means the technician charges a fixed amount of $50 for the repair.

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decrease 150 by 55 %

Answers

Answer:

Step-by-step explanation:

First calculate 55% of 150:

= 150 x 55/100

= 82.5 ans

Now decrease it from 150:

= 150-82.5

= 67.5 ans Hope it helps!!

A bowling alley and a skating rink both offer birthday party rentals. The bowling alley costs $5 per person plus a $15 room rental fee. The skating rink costs $3 per person plus a $20 room rental fee. You have $50. If you want to invite as many people as possible, which location should you choose?

Follow the steps to decide on the party location.

1. Write an expression for the amount you would spend on a birthday party at the bowling alley. Let x represent the number of people you invite. (2 points)















2. Write an expression for the amount you would spend on a birthday party at the skating rink. (2 points)















3. How many people could you invite to the bowling alley? Show how you found your answer. (2 points)















4. How many people could you invite to the skating rink? Show your work. (2 points)















5. To which location could you afford to invite more people? (2 points)

Answers

Answer:

I'll try my best B r u h ....

Step-by-step explanation:

Bowling:

15+5x  where x is the number of people

Skating:

20+3x

We have 50 dollars so the amount must be less than or equal to 50

Bowling

15+5x≤50

Subtract 15 from each side

15-15+5x≤50-15

5x ≤35

Divide each side by 5

5x/5 ≤35/5

x ≤7

She can have 7 or less people

Skating

We have 50 dollars so the amount must be less than or equal to 50

20+3x  ≤50

Subtract 20 from each side

20-20+3x  ≤50-20

3x  ≤30

Divide each side by 3

3x/3 ≤30/3

x ≤10

She can have up to 10 people

She can invite more people skating

Hope this helped.

999

What is the measure of z? X 4 Z 9 z= [?]V Give your answer in simplest form.​

Answers

Answer:

3√13

Step-by-step explanation:

4 : y = y = 9

y^2 = 36

y = 6

z = [tex]\sqrt{9^2 + 6^2} = \sqrt{81 + 36} = \sqrt{117}[/tex]

117 = 3^2 * 13

[tex]\sqrt{117} = \sqrt{3^2 * 13} = 3\sqrt{13[/tex]

write (-4x^2ya^3)^2 as a monomial in standard form

^ means exponent and the number after is the exponent
PLS HELP

Answers

Answer:

[tex]16x^4y^2 a^6[/tex]

Step-by-step explanation:

[tex](-4x^2ya^3)^2=(-4)^2(x^2)^2(y)^2(a^3)^2 \\ \\ =16x^4y^2 a^6[/tex]

Araceli earns $85,000 per year. Now that she has paid off her credit card debt, she is ready to buy a house. Araceli has a $200 car payment, no student loans, $300 in car insurance every 6 months and she estimates that her monthly utility bills will be $250 in her new house. If her bank requires no more than a 36% debt to income ratio, what would her maximum monthly mortgage payment be?

Answers

Answer:

$2300

Step-by-step explanation:

1. Her yearly allowable debt

36% × 85000 = 30600

2. Her monthly allowable debt

30600/12 = 2550

3. Her monthly existing debt

car payment = 200

car insurance = 300/6 =50

monthly utility bill = na this is an estimation

4. allowable debt - existing debt

2550 -200-50= 2300

ps: i may be wrong

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